Factor the following expression: $-9$ $x^2$ $-40$ $x$ $-16$
Explanation: This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(-9)}{(-16)} &=& 144 \\ {a} + {b} &=& & & {-40} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $144$ and add them together. The factors that add up to ${-40}$ will be your ${a}$ and ${b}$ When ${a}$ is ${-4}$ and ${b}$ is ${-36}$ $ \begin{eqnarray} {ab} &=& ({-4})({-36}) &=& 144 \\ {a} + {b} &=& {-4} + {-36} &=& -40 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {-9}x^2 {-4}x {-36}x {-16} $ Group the terms so that there is a common factor in each group: $ ({-9}x^2 {-4}x) + ({-36}x {-16}) $ Factor out the common factors: $ x(-9x - 4) + 4(-9x - 4) $ Notice how $(-9x - 4)$ has become a common factor. Factor this out to find the answer. $(-9x - 4)(x + 4)$